When \(g\)  and \(r\)  are powers of a prime \(p\)  and \(h \text{ (mod }p\text{)}\ne 1\)  and \(\lceil h/g\rceil \text{ (mod }p\text{)}\ne p-1\)  then [1]} can shave off a factor of \(n\)  to give \((n,r,h,a=1,g)\) -MR LRCs over fields of size \(O(n)^{h-\lceil h/g\rceil +g-2}\)  (when \(p=g=2\)  this gives the third row of our table).
